相关论文: Convergence and Optimization Results for a History…
We consider the minimizers of $L^{2}$-critical inhomogeneous variational problems with a spatially decaying nonlinear term in an open bounded domain $\Omega$ of $\mathbb{R}^{N}$ which contains $0$. We prove that there is a threshold…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
Nonconvex functionals with spherical symmetry are studied. Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation.
We prove local boundedness of generalized solutions to a large class of variational problems of linear growth including boundary value problems of minimal surface type and models from image analysis related to the procedure of…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…
This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the…
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
We will study an open problem pertaining to the uniqueness of minimizers for a class of variational problems emanating from Meyer's model for the decomposition of an image into a geometric part and a texture part. Mainly, we are interested…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…
This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an $L^2(\R)$ maximum principle, in the form of a new…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin space. Under an additional assumption…